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Quantitatively, the magnitude of the required centripetal force is related to the speed and radius of circular motion by the formula F=mv²/r.

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For the same v, a stronger centripetal force F would result in a tighter circular motion (smaller r). In the animation below, the objects are experiencing centripetal forces of 4F, 2F and F, resulting in circular motion of radii R, 2R and 4R.

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For the same centripetal force F, a lower speed v would result in a tighter circular motion (smaller r). In the animation below, the objects have speeds of 1/√2 v, v and √2v, resulting in circular motion of radii R, 2R and 4R.

• 06 Circular Motion